Foundations

QMA gives a polynomial-time quantum verifier a polynomial-qubit witness, accepting some witness on yes-instances and rejecting every witness on no-instances with a bounded completeness/soundness gap.

An interactive proof lets a polynomial-time randomized verifier exchange messages with a computationally unbounded prover.

The equality IP=PSPACE refers to polynomial-time randomized verification with polynomially many interactions and an unrestricted prover.

Zero knowledge requires an efficient simulator for the verifier's allowed view without the witness, with exact, statistical or computational indistinguishability as specified.

The PCP theorem expresses NP=PCP(O(log n),O(1)): a polynomial-time verifier uses logarithmically many random bits and queries a constant number of positions in a polynomial-length proof, with completeness one and bounded soundness such as one-half.

A proof assistant checks that a term establishes a formal proposition under declared axioms and kernel rules.

CompCert's principal semantic-preservation theorem relates accepted C abstract syntax to generated assembly abstract syntax: generated behavior refines permitted source behavior under the theorem's hypotheses.

The official CompCert 3.18 release in August 2026 revises formal handling of alignment/free and adds Rocq 9.2 support.

Types describe values and permitted operations; checks occur at different stages.